Evolution is the biological process primarily responsible for the rich diversity of Earth?s biota and is accomplished most prominently through natural selection (Darwin ¹⁸⁵⁹). The potential effect of selective pressures on any organism, and the form and function that a trait may realize, can be limited, however, by the current state and evolutionary history of that trait (Gould and Lewontin ¹⁹⁷⁹). Occasionally, students of evolution ?atomize? an individual into discrete and independent traits without considering how traits interrelate and influence the evolution of the entire organism. This tendency may lead to ingenious or fanciful explanations of the adaptive nature of a trait, and also to the misapprehension that all character states in nature are products of natural selection and exist as optima (Gould and Lewontin ¹⁹⁷⁹).

Of recent interest is the utility of imprecision in the waggle dance of the honey bee. The dance is an adaptation for social recruitment (Sherman and Visscher ²⁰⁰²; Dornhaus and Chittka ²⁰⁰⁴; Dornhaus et al. ²⁰⁰⁶) and is used to communicate the location of that resource relative to the position of the sun (von Frisch ¹⁹⁶⁷). The dance works as a ritualized reenactment of the foraging flight, in which the direction flown to a resource, relative to the sun?s azimuth, is indicated by the body orientation and movement of the dancing bee relative to ?up? on a vertical comb (Fig.?1). This phase of the waggle dance is called a waggle phase. After completing a waggle phase, a dancer returns to its origin via a return phase to perform another waggle phase. Distance is communicated through sound bursts produced during the waggle phase of the dance, the duration of which correlates to the distance of a resource (Wenner ¹⁹⁶²; Esch and Kerr ¹⁹⁶⁵; von Frisch ¹⁹⁶⁷).

There is considerable variation, however, in the direction communicated within a single dance (Haldane and Spurway ¹⁹⁵⁴; Wilson ¹⁹⁶²; von Frisch ¹⁹⁶⁷; Edrich ¹⁹⁷⁵; Gould ¹⁹⁷⁵; Towne ¹⁹⁸⁵; Towne and Gould ¹⁹⁸⁸; Weidenm?ller and Seeley ¹⁹⁹⁹). Though some of this error may be mitigated by the manner in which information from the dance is processed (Tanner and Visscher ²⁰⁰⁸). The angular difference in the direction between consecutive waggle phases is the divergence angle. Interestingly, the magnitude of the divergence angle has a negative relationship with the distance of a resource from the hive. Some authors contend that the divergence angle has evolved as an adaptation in temperate honey bees to distribute recruits across a resource patch (Wilson ¹⁹⁶²; Towne and Gould ¹⁹⁸⁸), and that the relationship between divergence angle and the distance of a resource from the hive represents a tuning to produce a recruit distribution of optimal size that remains constant with distance (Towne ¹⁹⁸⁵; Towne and Gould ¹⁹⁸⁸; Weidenm?ller and Seeley ¹⁹⁹⁹). A recent study of recruit distributions, however, showed that, at a distance of 250?m from the hive, the distribution of bees was significantly smaller than the imprecision in the dance would predict (Tanner and Visscher ²⁰⁰⁸). In this study, we test if the imprecision in the indication of distance and direction are sufficient to produce a distribution of recruits that will have the same spatial dimensions as a resource becomes increasingly distant. For a distribution to remain constant with distance, not only must the imprecision in direction decrease, but also the imprecision in distance communication must remain constant. An increase or decrease in variation will alter the size of the distribution.

To test what effect the distance of a resource has on the imprecision in the communication of direction and distance, and consequently on the distribution of recruits, we conducted an experiment in which bees were trained to feeders located 200, 400, 600, 800, and 1,000?m from the hive. We recorded the dances and dance sounds of these bees and compared the precision in these dances to models of dance error generated by the tuned-error hypothesis.

Figure?3 depicts the divergence angle to distance relationship that would result in arcs (i.e. the lateral distributions of bees) of equal width at all distances, as a family of iso-arc-length lines (gray lines). The black lines and points represent the data we collected and previously published data of Towne and Gould (¹⁹⁸⁸). The tuned-error hypothesis states that distributions of recruits, resulting from the imprecision in the dance, will have spatial dimensions that are constant despite the distance of a resource. If the imprecision in the dance is sufficient, then the data illustrated on Fig.?3 should follow a single iso-arc-length line. We show, however, that the distributions of bees (black lines), as predicted by dance information, do not track the iso-arc-lengths (gray lines).

The graph in the upper right of Fig.?3 plots an arc length (i.e. lateral distribution of bees) to distance relationship produced by holding divergence angle constant at the observed 500?m value (slanted dashed lines), and holding arc length constant with distance (horizontal light line), which represents the relationship predicted by the tuned-error hypothesis. Neither our, nor the data reported by Towne and Gould (¹⁹⁸⁸), fit the relationship predicted by the tuned-error hypothesis of constant arc length with distance. Instead, there are increasing arc lengths (i.e. increasing area over which recruits will be distributed) up to about 500?m, and then steady or decreasing arc lengths.

Figure?4 shows the relationship between sound burst duration and the distance of a resource, and Table?2 contains the results of the ANOVA. These results show that the distance of a resource has a significant effect on sound duration (F?=?158.9, P?<?0.0001), while all other effects were not significant.

The regression of variance in the dance against the distance of the resource from the hive was significant (r²?=?0.345, P?<?0.001), which is consistent with data presented in von Frisch (¹⁹⁶⁷). Figure?5 shows that the variance of sound duration increased with increasing distance.

We show that imprecision in dance communication does not fit specific trends predicted by the tuned-error hypothesis. While divergence angle in dances decreases as the distance of a resource increases, it does not decrease rapidly enough to create a spatial distribution of recruits that will remain constant (Fig.?3). Indeed, when resources are located within 500?m from the hive, a model of no change in divergence angle with distance fits the pattern of recruit distribution, as predicted by dance information, better than a model of the tuned-error hypothesis, suggesting that distributions of recruits would increase at a steady rate despite smaller divergence angles. Additionally, we show that the variation in distance communication increases significantly with distance, which may increase the distribution of recruits in the field. We note, however, that while this change in variation is significant, it is not large (Fig.?5). These data suggest that the error in the dance would produce distributions of recruits that noticeably increase in size with the distance of a resource from the hive. This trend was illustrated previously by Towne (¹⁹⁸⁵), who showed a distribution of bees covering an area of 9,920?m² at a distance of 100?m from the hive and 20,120?m² at 800?m from the hive, though these data were reported to support the tuned-error hypothesis by illustrating distributions of similar sizes at various distances from the hive.

In this study, we tested predicted distributions, and not actual distributions, of recruits against patterns predicted by the tuned-error hypothesis, though our data corroborate previous studies that show that recruit distributions do not fit specific patterns predicted by the tuned-error hypothesis (Towne ¹⁹⁸⁵; Tanner and Visscher ²⁰⁰⁸). We show here that the imprecision in the communication of direction does not decrease rapidly enough and imprecision in the communication of distance increases too much to generate patterns predicted by the tuned-error hypothesis. We suggest, therefore, that natural selection need not be invoked to explain imprecision in the honey bee dance language, but that it may be more simply explained as an adaptive constraint, and echo the remarks of Williams (¹⁹⁶⁶) on natural selection:

?This biological principle should be used only as a last resort. It should not be invoked when less onerous principles, such as those of physics and chemistry ? are sufficient for a complete explanation.?

We would like to acknowledge and thank Dr. Richard Redak, and Dr. John Klotz for their thoughtful review of this manuscript. We would also like to thank the Regents of the University of California and Graduate Student Association of UC Riverside for funding.

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